The Man Who Has Confidence In Himself Gains The Confidence Of Others. – **Hasidic Proverb**

*In this lecture,** I am discussing about** how to check continuity and discontinuity in a graph of a function through limits. I am using my own assignments to explain NCERT Exercise 5.1 Questions as well as Extra (HOTS) question for explanation and CBSE Board exam point of view. You can download assignments and all other material related to maths on my website. Questions Discussed in this lecture:*

1. \(f(x)=\begin{cases} kx^{2} & \text{ if } x\le 2 \\ 3& \text{ if } x>2 \end{cases} \)

2. \(f(x)=\begin{cases} kx+1& \text{ if } , x\le \pi \\ \cos x& \text{ if } , x>\pi \end{cases} \)

3. \(f(x)=\begin{cases} kx+1& \text{ if } , x\le 5 \\ 3x-5& \text{ if } , x>5 \end{cases} \)

4. \(f(x)=\begin{cases} \frac{x^{2} -2x-3}{x+1} , x\ne -1 \\ k, x=-1 \end{cases} \)

5. \(f(x)=\begin{cases} \frac{k\cos x}{\pi -2x} & \text{ if } , x\ne \frac{\pi }{2} \\ 3& \text{ if } , x=\frac{\pi }{2} \end{cases} \)

6. \(f(x)=\begin{cases} 5 & \text{ if } , x\le 2 \\ ax+b & \text{ if } , 2<x<10 \\ 21& \text{ if } , x\ge 10 \end{cases} \)

7. \(f(x)=\begin{cases} \frac{1-\cos 2x}{2x^{2} }, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} \)

8. \(f(x)=\begin{cases} \frac{log (1+ax)-log (1-bx)}{x}, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} \)

9. \(f(x)=\begin{cases} \frac{sin ^{2} kx}{x^{2} }, & \text{ if } x\ne 0 \\ 1, & \text{ if } x=0 \end{cases} \)

10. \(f(x)=\begin{cases} \frac{1-\cos 4x}{x^{2} }, & \text{ if } x<0 \\ k, & x=0 \\ \frac{\sqrt{x} }{\sqrt{16+\sqrt{x} } -4}, & \text{ if } x>0 \end{cases} \)

11. \(f(x)=\begin{cases} \frac{x}{|x|+2x^{2} }, & \text{ if } x\ne 0 \\ k, & \text{ if } x=0 \end{cases} \)